\section{1.15} 
\begin{frame}[allowframebreaks]{1.15. }

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{\color{red}1.15. PROPOSITION. }

Let $M^\bullet \in D^b(\mathcal{D}_X)$. 
Assume there exists a spectral sequence $(E_r)$ of $\mathcal{D}_X$-modules which converges to the graded module $\mathrm{gr}\,H^iM^\bullet$ associated to a finite filtration of $M^\bullet$ and that $E_s$ is holonomic for some $s$. 
Then $M^\bullet$ is holonomic.

In fact, $E_r$ is then holonomic for all $r \ge s$, hence $\mathrm{gr}\,H^iM^\bullet$ is holonomic too. 

Repeated use of 1.12 now shows that $M^\bullet$ is holonomic.

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